The present invention relates to an image compression device and method, and more particularly, to a fractal image compression device and method using a contractive transformation function.
Digital image compression methods can be generally classified into transformation coding methods and vector quantization methods. With transformation coding methods (e.g., Joint Photographers Expert Group (JPEG) standard), image data is transformed into another domain, and compressed in the transformed domain. With vector quantization methods, a portion of image data is compared with images of a predetermined code book, and an index of the most similar code book image is then transmitted, thereby having a compression effect on the image data. Fractal image compression methods, as compared to the existing compression methods, approximate large quantities of digital image data by using a simple mathematical model, thereby having a compression effect on the image data.
With fractal image compression theory, one assumes that the image to be compressed is a fractal image having the property of self-similarity as the spatial scale is changed over several orders of magnitude. The property of self-similarity can be seen with, for example, a rocky, jagged coastline which looks similar when seen from a jet airplane (a distance of 10 km), from a low altitude plane (100 m) and from a standing position (1 m). Accordingly, for purposes of image processing, a contractive transformation function using the fractal image as an attractor can be obtained, thus compressing the image. It is very difficult, however, to obtain the contractive transformation function using the entire image to be compressed as the attractor. To resolve this problem with the fractal image compression method, the entire image is divided into a plurality of non-overlapping range blocks, and further divided into a plurality of domain blocks each having a size that is an integer (e.g., four) times larger than the size of each of the range blocks. The contractive transformation function for each one of the divided range blocks is obtained by contractively transforming the domain blocks into each of the range blocks, and calculating the errors between the contractively-transformed domain blocks and each of the range blocks. The domain block having a minimum error value for each range block is referred to as a matching domain block.
Jacquin's method is typically known as the most representative fractal image compression method based upon the method described above. In order to reduce the compression period, Jacquin's method classifies range blocks and domain blocks into several classes according to their attributes, and then, only the domain blocks belonging to the same class as a corresponding range block to be compressed are evaluated.
The fractal image compression method, which is theoretically capable of a very high-level of compression (i.e., 1/10,000), is an unsymmetrical process having a much shorter recovery period than compression period. Therefore, there is an advantage in that the fractal image compression method is useful in applications where high-speed image recovery is required.
Currently, an iterated function system (IFS) proposed by Barnsley et al. is being utilized as a fractal image compression device and method. This system is disclosed in detail in U.S. Pat. No. 5,347,600 entitled Method And Apparatus For Compression And Decompression Of Digital Image Data. The distortion measurement, which is used as a reference for determining the self-similarity characteristic between blocks in conventional fractal image compression devices and methods, is generally a mean square error (MSE). That is, the domain block having the minimum mean square error for a corresponding range block is determined to be the domain block having the best self-similarity characteristics. With many improved techniques for fractal image compression, the mean square error has been used for the distortion measurement between image blocks.
The similarity between image blocks and overall image quality, however, is ultimately determined by the perceptions of the human eye. In this context, use of the mean square error (MSE) has often presented problems in other image compression fields. Therefore, with conventional fractal image compression techniques, since the mean square error (MSE) does not always adequately reflect human visual properties, domain blocks that fail to provide "self-similarity" from a visual standpoint are often determined to be matching domain blocks. Accordingly, the quality of a recovered image may be numerically improved, but is visually deteriorated. Moreover, conventional fractal image compression techniques often provide a reduced compression rate due to unnecessary division of range blocks.